Solution:
For an m×n chessboard there are 2m+2n−2 ways.
Case I. There are two horizontally adjacent squares of the same color: 2m−2 ways.
Case II. There are two vertically adjacent squares of the same color: 2n−2 ways.
Case III. None of the...
Green dyes =5
Blue dyes =4
Red dyes =3
The no of ways of choosing of at least one green and one blue is =(25−1)×(24−1)×23
⇒(32−1)×(16−1)×8
⇒31×15×8
⇒3720
Total combination of balls = 212
Combination of balls with no green balls = 27
Combination of balls with no blue balls = 28
Combination of balls with no blue balls and no green...